198 REASONING. 



attribute mortality. Or if both the premises are general pro- 

 positions, as 



All men are mortal, 



All kings are men, 

 therefore 



All kings are mortal, 



the minor premise asserts that the attributes denoted by king- 

 ship only exist in conjunction with those signified by the word 

 man. The major asserts as before, that the last-mentioned 

 attributes are never found without the attribute of mortality. 

 The conclusion is, that wherever the attributes of kingship are 

 found, that of mortality is found also. 



If the major premise were negative, as, No men are omni- 

 potent, it would assert, not that the attributes connoted by 

 "man" never exist without, but that they never exist with, 

 those connoted by " omnipotent :" from which, together with 

 the minor premise, it is concluded, that the same incompati- 

 bility exists between the attribute omnipotence and those con- 

 stituting a king. In a similar manner we might analyse 

 any other example of the syllogism. 



If we generalize this process, and look out for the prin- 

 ciple or law involved in every such inference, and presupposed 

 in every syllogism, the propositions of which are anything more 

 than merely verbal; we find, not the unmeaning dictum 

 de omni et nullo, but a fundamental principle, or rather two 

 principles, strikingly resembling the axioms of mathematics. 

 The first, which is the principle of affirmative syllogisms, 

 is, that things which coexist with the same thing, coexist 

 with one another. The second is the principle of negative 

 syllogisms, and is to this effect : that a thing which coexists 

 with another thing, with which other a third thing does not 

 coexist, is not coexistent with that third thing. These axioms 

 manifestly relate to facts, and not to conventions ; and one or 

 other of them is the ground of the legitimacy of every argu- 

 ment in which facts and not conventions are the matter 

 treated of.* 



* Mr. Herbert Spencer (Principles of Psychology, pp. 125-7), though his 

 theory of the syllogism coincides with all that is essential of mine, thinks it a 



